Question

Triangle WXY, with vertices W(-9,-8), X(-2,-6), and Y(-8,-2), is drawn inside a rectangle.What is the area, in square units, of triangle WXY?

Answer 1

To find the area of triangle WXY, we can use the formula for the area of a triangle:

Area = 1/2 * base * height

First, we need to find the base and height of triangle WXY. We can do this by finding the distance between the coordinates of the vertices.

The distance between points W and X can be found using the distance formula:

d = √[(x2 - x1)^2 + (y2 - y1)^2]

d = √[(-2 - (-9))^2 + (-6 - (-8))^2]
d = √[7^2 + 2^2]
d = √[49 + 4]
d = √53

The distance between W and X is √53 units.

Similarly, the distance between points W and Y can be found:

d = √[(-8 - (-9))^2 + (-2 - (-8))^2]
d = √[1^2 + 6^2]
d = √[1 + 36]
d = √37

The distance between W and Y is √37 units.

Now we can use the base and height to find the area of triangle WXY:

Base = √53
Height = √37

Area = 1/2 * √53 * √37
Area = 1/2 * √(53 * 37)
Area = 1/2 * √(1961)
Area = 1/2 * √1961
Area ≈ 22.209 square units

Therefore, the area of triangle WXY is approximately 22.209 square units.